1. Industrial Field of the Invention
The present invention relates to a method of executing numerical simulation for simulating a physical phenomenon such as heat, fluid, physical structure, and electro-magnetic field by a computer. More particularly the present invention relates to a method of executing numerical simulation capable of reducing the number of simulation steps with simpler inputs to be designated.
2. Description of the Related Art
Numerical simulation is widely used in industrial fields as a method of simulating a physical phenomenon such as heat conduction, fluid flow and physical structure by using a computer. By using numerical simulation, it is possible to reproduce and observe a physical phenomenon and determine design parameters, without actual experiments using a model and apparatus. It can be expected therefore that design time and cost can be reduced considerably.
The principle of numerical simulation is to numerically solve equations describing a physical phenomenon by a computer. Such equations are generally ordinary differential equations and partial differential equations. As a means for numerically solving such equations, there are known the finite element method, the finite difference method and the like. In each of these methods, a number of representative points (nodes or grid points) are arranged within a region to be analyzed in which a subject physical phenomenon occurs, and the physical quantities such as temperature and fluid velocity continuously changing in the region are represented by sets of values at these nodes. An original differential equation is replaced by a set of linear equations representing values at these nodes. Such replacement of continuously changing values by a finite number of values at nodes, is called "discretization", and a set of nodes is called a "mesh". In order to analyze a phenomenon changing with time, it is necessary to calculate equations at the interval of time step, irrespective of continuously changing time.
In order to execute numerical simulation by a computer, it is necessary to provide a program which instructs the computer the detailed algorithms of simulation, involving a good understanding of mathematical and programming techniques. In view of this, in many cases most users obtain a commercially available program and input thereto necessary data and instructions to execute numerical simulation. A program of this type is called a numerical simulation package. There are two types of such a package. In one type, a numerical simulation program is automatically generated upon input of differential equations, boundary conditions and the like. This type is called hereinafter a variable-equation type simulation package. The variable-equation type package has the advantage that different types of problems can be dealt with by inputting different differential equations or combinations of such different differential equations. However, it requires programming and discretization knowledge in order for a user to become an expert. An example of the variable-equation type package is disclosed in C. Konno, et al. "Advanced Implicit Solution Function of DEQSOL and its Evaluation", Proceedings of the Fall Joint Computer Conference, pp. 1026 to 1033, (1986). In the other type, a physical phenomenon which can be analyzed (i.e., differential equations to be solved) is fixedly determined, and data specific to the phenomenon is inputted to execute numerical simulation. This type is called a fixed-equation type simulation package. This fixed-equation type package is not required to supply equations. However, since a physical phenomenon to be dealt with is fixed, other physical phenomena or a combined simulation with other physical phenomena cannot be dealt with. Accordingly, a user is requested to select a proper package by checking whether a subject problem is within the range of application fields of the package. An example of the fixed-equation type simulation package is PHONECS of CHAMP Ltd., England. PHONECS is described in detail in PHONECS--beginners's guide and user manual by H. I. Rosten and D. Brian Spalding, CHAM TR/100, 1986, pp. 24 to 37.
A user is required to designate the kind of numerical algorithms (or numerical value calculation procedures), regardless of which type of a simulation package the user selects. Most physical phenomena include time dependency and non-linearity. Various methods are known to process such time dependency and non-linearity for numerical simulation. Accordingly, most simulation packages are structured to allow selective use of such methods. However, a user must determine which one or which combination of the methods is to be used. Furthermore, even after determining proper algorithms, a user must set the arrangement of nodes and a time step in order to execute proper simulation.
Many attempts have been made to provide users with numerical simulation packages easy to use. In U.S. Pat. No. 4,742,473 by Shugar, there is disclosed a method in which a simulation package using the finite element method is provided with a menu-type interface, and attributes (material constants, boundary conditions and the like) are set to nodes or elements on a mesh by using an intelligent cursor on a screen. In JP-A-2-151927 corresponding to U.S. patent application Ser. No. 07/443,252, now U.S. Pat. No. 5,148,379 assigned to the present assignee, there is described a method in which a user refers to guidances and selects a combination of key indices to automatically generate a program for numerical simulation. The structure of guidances is shown in FIG. 11 of its specification. The guidances has a hierarchical structure such that when a user chooses one selection item, the relevant lower level selection items are displayed to urge the user to further choose one of them. For example, a user chooses one of selection items (such as heat conduction, diffusion, and fluid flow) regarding a physical phenomenon name, the selected one corresponding to the physical phenomenon the user wishes to simulate. If a fluid flow is selected, selection items "laminar flow or turbulent flow" and "compressible or incompressible" regarding classification of fluid flow phenomena are displayed for the user. If a laminar flow is selected, then selection items "steady or transient" and "linear or non-linear" regarding a simulation condition of the laminar flow are displayed for the user. Until all indices are determined by the user, displaying selection items and selecting them by the user are repeated. In accordance with a combination of selected key indices (e.g., "fluid flow, laminar flow, transient, and implicit method"), an algorithm database is searched to retrieve numerical algorithms for a problem to the solved.
The technique disclosed in the above-cited U.S. Pat. No. 4,742,473 does not consider how a user selects a simulation package which can deal with a plurality of physical phenomena (i.e., partial differential equations) and numerical algorithms. A user must select equations and numerical algorithms from knowledge the user has.
In the case of the technique disclosed in the above-cited JP-A-2-151927 corresponding to U.S. patent application Ser. No. 07/443,252, a user must select key indices for the kind of physical phenomena and numerical algorithms. The technique does not consider a user who is not accustomed with selecting key indices and has poor mathematical techniques. Therefore, a user is requested to understand the meanings of key indices and its selection method very well.
In the case of the techniques disclosed in the above-cited U.S. Pat. No. 4,742,473 and JP-A-2-151927 corresponding to U.S. patent application Ser. No. 07/443,252, a user must determine the arrangement of nodes and a time step which act an important role in obtaining a correct solution of simulation.